Please be detailed with your answer Thank you The diagrams a

The diagrams above show possible wavefunctions for a particle \"trapped n a finite potential well. Note that the total particle energy is less than the value of the potential at the top of the well and that the bottom of the potential well is not flat. Also note that only diagram Ahas the wavefunction at zero at the boundaries. State which one of the four diagrams could be a correct sketch of the wavefunction. Briefly explain what is incorrect for each of the other three.

Solution

Diagram C is correct

The potential is finite. Therfore, the wavefunction must penetrate the box at certain level. But in figure A, it vanishes at the boundary. hence A is wrong..

The wavefunction must have single vaue for particular value of position. But it has more than one value. So option D is wrong.

The potential is slowly varying. It does not produce any effect on the wavefuncion. Hence option B is wrong.

The digram C is correct. Because the effect of potential is observed in the wavefunction.